euler_linear

std.seq.euler_linear · Level L2

Integrate x′ = A·x from x₀ by forward Euler over the time steps dts; returns the state after every step. A Scan of euler_step.

xₜ₊₁ = xₜ + dtₜ·A·xₜ

Signature

euler_linear(x0: f64[k], A: f64[k, k], dts: f64[n]) → f64[n, k]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

x0f64[k]Af64[k, k]dtsf64[n]Scan·euler_stepXXf64[n, k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x = x0; for each dt: x = x + dt * (A @ x) in exact rational arithmetic, on all 40 test cases.
  • All 533 float64 results inside the running error bound; the closest uses 58% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
70%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
86

Large ulp counts appear only where cancellation drives a result toward zero; the absolute error is still inside the bound.

Identity

Calls
euler_step
Called by
—
sha256:5a9a9b87a3fb9d0929353f47bf7f95cda74549bac1962aa7b92a9e18227459e9

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.